The investigation of the flag-transitive 2-\((k^{2},k,\lambda )\)  designs,
with \(\lambda \mid k\) , has been recently started in [1]}. The reason of studying such 2-designs is that they represent a natural generalization of the affine planes in
terms of parameters, and also because, it is shown in [2]} that, the blocks of imprimitivity of a family of flag-transitive, point-imprimitive symmetric 2-designs investigated in [3]} have the structure of the 2-designs analyzed here.
It is shown in [1]} that, apart from the smallest Ree group, a
flag-transitive automorphism group \(G\)  of a 2-\((k^{2},k,\lambda )\)  design \(\mathcal {D}\) , with \(\lambda \mid k\) , is either an affine group or an almost
simple classical group. Moreover, when \(G\cong ~^2 G_{3}(3)\) , the
smallest Ree group, \(\mathcal {D}\)  is isomorphic either to the 2-\((6^{2},6,2)\)  design or to one of the three 2-\((6^{2},6,6)\)  designs
constructed in [1]}. All the four 2-designs have the 36 secants of
a non-degenerate conic \(\mathcal {C}\)  of \(PG_{2}(8)\)  as a point set and 6-sets of secants in a remarkable configuration as a block set. Clearly, \(G\cong ~^2 G_{3}(3)\)  is a special case of an almost simple
classical group, since \(~^2 G_{3}(3)\cong P\Gamma L_{2}(8)\) .
